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Completing Multiparticle Representations of the Poincaré Group.

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Researchers introduce new quantum numbers, pairwise helicities (q_ij), to define complex multiparticle states beyond simple one-particle combinations. This advances S-matrix theory for scattering phenomena.

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Area of Science:

  • Theoretical Particle Physics
  • Quantum Field Theory
  • Scattering Theory

Background:

  • Standard S-matrix theory defines asymptotic multiparticle states as tensor products of single-particle states.
  • Existing formalisms face challenges in fully describing complex scattering scenarios involving multiple interacting particles.

Purpose of the Study:

  • To extend the definition of asymptotic multiparticle states in S-matrix theory.
  • To introduce and define novel quantum numbers, termed pairwise helicities, for asymptotically separated particle pairs.
  • To generalize existing constructions to accommodate these new states and their associated quantum numbers.

Main Methods:

  • Generalized the Wigner construction to independently treat single particles and particle pairs.
  • Introduced pairwise helicities (q_ij) as new quantum numbers characterizing particle pair interactions.
  • Projected generalized states onto physical states, analyzing their behavior under specific conditions (vanishing q_ij, vanishing spins).

Main Results:

  • Developed a new framework for asymptotic multiparticle states that goes beyond simple tensor products.
  • Demonstrated that the new states reduce to standard tensor product states when pairwise helicities vanish.
  • Showed that vanishing spins reproduce Zwanziger's scalar dyon states, validating the construction.
  • Identified pairwise helicity as q_ij = e_i*g_j - e_j*g_i for scattering of electric and magnetic charges.

Conclusions:

  • The proposed extension provides a more comprehensive description of asymptotic multiparticle states.
  • Pairwise helicities offer a new perspective on the quantum numbers governing particle interactions in scattering.
  • The construction successfully describes the asymptotic states for scattering involving electric and magnetic charges.